Copying animation keyframes from one bone to another with flipping
Figured out how to mirror the same animation keyframes to the other bone hand, without any re-work or manual labor required.

With the animated hand's bone rig selected, select all the keyframes in the Timeline (Shift+F12 to get the Timeline view and use your mouse to box-select them all or press Ctrl+A) and copying them with Ctrl+C.



Then proceeded to select the other hand's bone rig (the non-animated one). With the non-animated bone, first setup at least one initial keyframe in the timeline. I did this with hitting i to put in an initial keyframe.

Lastly, the trick to get the animation pasted and flipped for this other hand bone is to have the Graph Editor open (Shift+F6) and right click in it and press Paste_Flipped (or alternatively press Shift+Ctrl+V).



Done! Now the other previously non-animated hand bone rig is now animated with the exact same keyframes as the other hand, just flipped so it looks correct!
This was all done whilst in Pose Mode.